At mealtimes, the evaluation of the appropriate (or not appropriate) behavior concerning the food is often assumed as a topic of discourse. The aim of this study is to single out the argumentative strategies used by parents with their children and by children with their parents in order to convince the other party to eat or not to eat a certain food. Within a data corpus constituted by 30 video-recorded meals of 10 middle to upper-middle-class Swiss and Italian families, we selected a corpus of 77 argumentative discussions between parents and children arisen around a food-related issue. Data are presented through discursive excerpts of argumentative discussions that were found within the data corpus and analyzed through the pragma-dialectical model of critical discussion. The results of this study show that the feeding practices in families with young children during mealtimes are argumentatively co-constructed by participants. In most cases parents put forward arguments based on the quality (e.g., very good, nutritious, salty, or not good) and quantity (e.g., too little, quite enough, or too much) of food to convince their children to eat. Similarly, children put forward arguments based on the quality and quantity of food to convince their parents to change their standpoint, although their view on the issue is the opposite of that of their parents.